To prove (REF ) we use induction on \(|\beta |\) . Firstly, consider the case \(|\beta |=0\) . We modify the proof of Lemma 2.4.4 of [1]}. Denote \(r_0=s\)  and \(r_m=s+(r-s)\sum _{j=1}^m2^{-j}\)  for \(m=1,2,\cdots \) .
choose a smooth function \(\zeta _m\)  so that \(0\le \zeta _m\le 1\) ,
\(\zeta _m=1 \quad \text{on} \quad U_{r_m}, \quad \quad \zeta _m=0 \quad \text{on}\quad \Omega \setminus U_{r_{m+1}},\) 
\(|\zeta _{mx}|\le N (r-s)^{-1}2^m, \quad |\zeta _{mxx}|\le N(r-s)^{-2} 2^{2m},\quad |\zeta _{mt}|\le N (r-s)^{-2} 2^{2m}.\) 
